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1
Prepare the Cake: Preheat oven to 350u00b0F. Combine boiling water, cocoa, unsweetened chocolate, and, if desired, instant coffee in a bowl. Let stand 2 minutes; whisk until smooth. Let cool completely.
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2
Whisk together flour, baking powder, and salt in a bowl. Beat butter with an electric mixer at medium speed until smooth, about 1 minute. Add brown sugar and 1 cup granulated sugar; beat until light and fluffy, about 2 minutes. Add eggs, 1 at a time, beating well after each addition. Beat in sour cream and 1 teaspoon vanilla. Add flour mixture to butter mixture alternately with cocoa mixture, in 5 additions, beginning and ending with flour mixture. Beat at medium speed until smooth, about 1 minute. Divide batter evenly between 2 (9-inch) greased and floured round cake pans. Bake in preheated oven until a wooden pick inserted in the center comes out clean, 28 to 32 minutes. Cool in pans on a wire rack 10 minutes. Remove cake from pans; cool completely, about 30 minutes.
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3
Prepare the Coconut Cream Filling: Stir together half-and-half and shredded coconut in a small saucepan over medium; bring just to a boil. Remove pan from heat; let stand 30 minutes. Pour mixture through a fine wire-mesh strainer into a bowl, pressing on solids; discard solids. Return coconut liquid to pan; bring to a simmer. (Coconut liquid should just begin to bubble around the edges of pan.) Whisk together 5 tablespoons granulated sugar, cornstarch, and egg yolks in a medium bowl until smooth. Gradually add hot coconut liquid to egg mixture, whisking constantly. Return mixture to pan. Cook, whisking constantly, over medium heat until thick and bubbly, 5 to 6 minutes. Remove pan from heat. Whisk in 2 tablespoons butter, rum, 1 teaspoon vanilla, and coconut extract. Pour mixture into a shallow dish; refrigerate until completely cold, about 2 hours. Transfer chilled custard to a medium bowl.
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4
Beat 1/2 cup heavy cream until stiff peaks form. Gently fold whipped cream into custard in 2 batches. Refrigerate until ready to use.
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5
Prepare Chocolate Frosting: Combine 2 cups heavy cream and powdered sugar in a medium saucepan. Bring to a simmer over medium. (Do not boil.) Place bittersweet chocolate in a medium bowl; pour hot cream mixture over chocolate. Let stand 1 minute; gently stir until all of the chocolate melts and mixture is smooth. Chill until mixture thickens to spreading consistency, 30 to 40 minutes, stirring every few minutes.
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6
To assemble cake, slice cake layers in half horizontally using a serrated knife; place 1 layer, cut side up, on a plate. Spread about 1/4 cup Chocolate Frosting over top. Top with one-third of Coconut Cream Filling, leaving a 1/2-inch border. Top with another cake layer; repeat layers twice, beginning with frosting and ending with a cake layer. Spread remaining Chocolate Frosting on top and sides of cake. (If chocolate gets too thick to spread, microwave at HIGH until spreadable, 5 to 7 minutes.) Press unsweetened flaked coconut around sides of cake.
